In golf, the desired putt is always a straight putt, with the lay of the land and speed of the ball controlling the break. Most experienced golfers can visualize the line of the stroke that the ball should take. Their problem is getting the ball to travel the intended line. They may twist and close, or open and push the ball, but not strike the ball squarely to propel it along the visualized line. If the putt is short, even an unsquare hit can sink the ball. For longer putts, though, a square hit is essential.
In billiards or pool, a ball squarely hit, with the tip of the cue stick on its vertical centerline will travel a straight line. In order to make it go along its intended line, the cue must be driven axially smoothly through the ball on that line. Practice creates muscle and eye "memory" that enables repetition of a good, clean shot, time after time. It is easier to perfect cue stick shots, than putter shots. If the tip of the cue stick hits the ball at an angle, it will not go straight, even over short distances.